“I care much more about what we do than what we are called,” Kraninger told CFPB employees in an email obtained by The Hill.

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Mulvaney insisted the agency be called the Bureau of Consumer Financial Protection, its formal name under the 2010 Dodd-Frank law. But an internal agency analysis of the name-change, first reported by The Hill, found that rebranding could cost businesses about $300 million.

The CFPB in March released a new logo that referred to the agency as the Bureau of Consumer Financial Protection, and in June changed the sign in the front lobby of its Washington, D.C., headquarters to reflect the name change.

Kraninger cited the high financial toll and “operational challenges” of the name-change in her Wednesday email.

“While I certainly understand why [Mulvaney] emphasized following the letter of the law, I also understand that there are a variety of issues to take into consideration," she wrote, adding that the bureau will continue to use Mulvaney’s preferred name and a new seal reflecting it for official reports, legal filings “and other items specific to the office of the Director.”

But the bureau would use CFPB on all other public-facing materials, Kraninger said.

“In other words, we have a legal name but will be using our colloquial name and the branded acronym ‘CFPB.’ Many of us have legal names but use nicknames without much confusion,” Kraninger wrote, noting that she goes by ‘Kathy’ instead of ‘Kathleen’, her legal name.

Critics of the CFPB’s name-change efforts have noted that Mulvaney’s full name is “John Michael Mulvaney,” but he prefers to go by “Mick.”

Mulvaney, who's now acting chief of staff at the White House, had said the name change reflected his desire to drastically rein in the CFPB.

"We changed the name because it’s the name in the statute," Mulvaney said in June. "And if ... your whole theme is going to be, 'We’re going to follow the statute,' I thought it was a good, small way, but a very visible way, to send a message."While the Dodd-Frank Act named the agency as the Bureau of Consumer Financial Protection, it also makes several references to the Consumer Financial Protection Bureau.